Simplify the following expression: $k = \dfrac{8p^2 + 24p - 32}{p + 4} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $8$ , so we can rewrite the expression: $ k =\dfrac{8(p^2 + 3p - 4)}{p + 4} $ Then we factor the remaining polynomial: $p^2 + {3}p {-4} $ ${4} {-1} = {3}$ ${4} \times {-1} = {-4}$ $ (p + {4}) (p {-1}) $ This gives us a factored expression: $\dfrac{8(p + {4}) (p {-1})}{p + 4}$ We can divide the numerator and denominator by $(p - 4)$ on condition that $p \neq -4$ Therefore $k = 8(p - 1); p \neq -4$